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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-3 of 1024 Utah State University Located in Logan, Utah, USA 80 miles North of Salt Lake City 22,000 students study at USU’s Logan campus, nestled in the Rocky Mountains of the inter-mountain west CSOIS is a research center in the Department of Electrical and Computer Engineering

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-6 of 1024 CSRA Research: Center for Self-Organizing and Intelligent Systems CSOIS is a research center in USU’s Department of Electrical and Computer Engineering that coordinates most CSRA (Control Systems, Robotics and Automation) research Officially Organized Funded for 7 (seven) years by the State of Utah’s Center of Excellence Program (COEP) Horizontally-Integrated (multi-disciplinary) –Electrical and Computer Engineering (Home dept.) –Mechanical Engineering –Computer Science Vertically-integrated staff (20-40) of faculty, postdocs, engineers, grad students and undergrads Average over $2.0M in funding per year since 1998 Three spin-off companies since 1994.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-41 of 1024 How to Decide and ? we build two tables of optimal ITAE and ISE, respectively, with respect to and which are enumerated from 0.5 to 1.5 with step of 0.1

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-54 of 1024 Observations from Example-1 The best FO PID outperforms the best IO PID The best FO PI outperforms the best IO PI and The best FO PI outperforms the best IO PID

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-64 of 1024 Observations from Example-2 Fractional order boundary controllers are applicable. The best fractional order boundary controller are better than the best integer order boundary controller when the wave equation is time-fractional. Note: Boundary controllers considered in this example are still in very simple forms. How to design best fractional order controllers structures best suited for the fractional wave equation will be a new future research topic.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-71 of 1024 Big Picture, or, the message for you to take home the big picture for the future is the intelligent control of biomimetic system using biomimetic materials with fractional order calculus embedded. In other words, it is definitely worth to have a look of the notion of ``intelligent control of intelligent materials using intelligent materials.'' Advocating this picture is the major purpose or contribution, if any, of this talk.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-72 of 1024 Ubiquitous (2) – Independent Loopshaping? A Conjecture It is well known due to Bode that, for finite dimensional linear time invariant single input and single output rational systems, the gain and phase are inter-related. For robust loop shaping, it is not possible to do loopshaping for gain and loop phase plots independently. However, using fractional order control, this is possible. In other words, fractional order controllers have the potential to do loopshaping of phase and gain independently.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-76 of 1024 Question on “waterbed effect” In infinite dimensional setting, will this “waterbed effect” be invalid? If yes, it is a good news for FOC. But I do not know. Maybe. We need mathematicians to handle this research question. It is “yes” for nonlinear controls that have been shown to break the famous (curse?) “waterbed effect”.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-79 of 1024 FO PI/D tuning: research questions How to tell there is a need to use FO PI/D controller while integer order PI/D control works well in the existing controlled systems. How to predict the performance gain by using FO PI/D controller? How to best tune the FO PI/D controller by taking minimum experimental efforts? How to best design the experiments to tune FO PI/D controller? For a given class of plants to be controlled, how to best design FO PI/D controller? Concepci´on Alicia Monje Micharet. “Design Methods of Fractional Order Controllers for Industrial Applications”. PhD thesis, University of Extremadura, Spain, 2006.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-80 of 1024 Ubiquitous (4) – “mentally low cost” Robust Control Robustness is a “ubiquitous” requirement. Many existing robust control methods (H_infinity, LMI, H_2, SSV mu synthesis etc.) are “mentally expensive” to understand and follow by busy engineers. CRONE provided a “mentally low cost” robust control easily accepted by practitioners. It has been very successful and impressive. People may worry about the approximation implementation of FOC. The rationale here is: The robust controller C is designed to attack the uncertainty  P of the plant P. However, when implementing C, we introduced another  C. See this paper for the issue –I. H. Keel and S. Bhattacharyya. “Robust, fragile, or optimal?” IEEE Trans. on Automatic Control, 42: , So, a more authentic analog FOC element might relief this worry? Or, let us think in this way – “Low cost (analog) robust control with fractional element”. So, shall we convert the robust controller obtained from “expensive” design techniques to “low cost analog robust controllers using FOC element”? Maybe logical. YangQuan Chen. “Fractional Future?”. A Panel Discussion NSF Sponsored Joint France-US Workshop on Fractional Derivatives and Their Applications (FDTA). July 22-23, 2004, Bordeaux, France

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-81 of 1024 Ubiquitous (4.5) – A FAQ A FAQ is “Ya-- ! Your FOC (or fractional order filters) is good and interesting but in the end you need to implement it in finite dimensional transfer function (filter) of a high order. Why not simply start with the high order finite dimensional TF?” (implied suspicion: FOC is kind of redundant) Answers: –Less tuning knobs (engineers like this) –More insights (note: finite dimensional, lumped parameter modeling, analysis, control is just “for our own convenience”) –Etc. (e.g., “mentally economic?!”)

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-91 of 1024 Big picture of nanoparticle manufacturing Now: given cycles, given stroke profile, see how particulate process evolves. Future: Production process development – given final particle grain size distribution, how to achieve this by using minimum number of cycles with possible cycle-to-cycle, or run-to-run (per several cycles) adaptive learning control with variable stroke profiles.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-94 of 1024 Ubiquitous (6) – Long Range Dependence and FOSP Consider a second order stationary time series Y = {Y (k)} with mean zero. The time series Y is said to be long-range dependent if FOSP: fractional order signal processing

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-95 of 1024 Hurst parameter The Hurst parameter H characterizes the degree of long- range dependence in stationary time series. A process is said to have long range dependence when Relationships: 1), 2), d is the differencing parameter of ARFIMA

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-98 of /f noise Models of 1/f noise were developed by Bernamont in 1937: where C is a constant, S(f) is the power spectral density. 1/f noise is a typical process that has long memory, also known as pink noise and flicker noise. It appears in widely different systems such as radioactive decay, chemical systems, biology, fluid dynamics, astronomy, electronic devices, optical systems, network traffic and economics

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-100 of 1024 We may define 1/f noise as the output of a fractional system. The input could be white noise. Also, we can consider 1/f noise as the output of a fractional integrator. The system can be defined by the transfer function with impulse response Therefore, the autocorrelation function of the output is

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-101 of 1024 Fractional Gaussian Noise (fGN) fGN is a kind of 1/f noise. fGN can be seen as the unique Gaussian process that is the stationary increment of a self-similar process, called fractional Brownian motion (fBM). The fBM plays a fundamental role in modeling long-range dependence processes. The increments time series of the fBM process B H are called fGN.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-108 of 1024 Lyapunov’s Direct Method Enables one to determine whether or not the equilibrium state of system (#) is stable without actually determining the solution. Involves finding a suitable scalar function V(x,t) and examining its time derivative along the trajectory of the system.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-111 of 1024 Power Law Lyapunov Method Enables one to determine whether or not the equilibrium state of system (#) is stable without actually determining the solution. Involves finding a suitable scalar function V(x,t) and examining its time derivative along the trajectory of the system.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-114 of 1024 Intuitions You don’t have to be rich to be smart. You don’t have to be smart to use fractional order calculus. A dynamic system doesn’t have to make the “generalized energy” decay exponentially to be stable!A dynamic system doesn’t have to make the “generalized energy” decay exponentially to be stable! Call for Power Law Lyapunov Method

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-122 of 1024 Plenary Lecture #5 Abstract There is an increasing interest in dynamic systems and controls of noninteger orders or fractional orders. Clearly, for closed-loop control systems, there are four situations. They are 1) IO (integer order) plant with IO controller; 2) IO plant with FO (fractional order) controller; 3) FO plant with IO controller and 4) FO plant with FO controller. However, from engineering point of view, doing something better is the major concern. This talk will first show an example that the best fractional order controller outperforms the best integer order controller. Then, we try to argue why consider fractional order control even when integer (high) order control works comparatively well. We will also address issues in fractional order PID controller tuning. Using several real world examples, we further argue that, fractional order control is ubiquitous when the dynamic system is of distributed parameter nature.

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-124 of 1024 Dr YangQuan Chen is presently an assistant professor of Electrical and Computer Engineering Department and the Acting Director for CSOIS (Center for Self-Organizing and Intelligent Systems at Utah State University. He obtained his Ph.D. from Nanyang Technological University, Singapore in 1998, an MS from Beijing Institute of Technology (BIT) in 1989 and a BS from University of Science and Technology of Beijing (USTB) in Dr Chen has 12 US patents granted and 2 US patent applications published. He published many academic papers and (co)authored more than 50 industrial reports. His recent books include “Solving Advanced Applied Mathematical Problems Using Matlab” (with Dingyu Xue, Tsinghua University Press. August pages in Chinese. ISBN /O.392), "System Simulation Techniques with Matlab/Simulink" (with Dingyu Xue, Tsinghua University Press, April 2002, ISBN /TP3137, in Chinese) and "Iterative Learning Control: Convergence, Robustness and Applications" (with Changyun Wen, Lecture Notes Series in Control and Information Science, Springer-Verlag, Nov. 1999, ISBN: ).

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7/21/2006 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal Slide-125 of 1024 His current research interests include autonomous navigation and intelligent control of a team of unmanned ground or aerial vehicles, distributed real-time irrigation control, distributed parameter system controls with MAS-net (mobile actuator- sensor networks), fractional order control and signal processing, interval computation, and iterative/repetitive/adaptive learning control. Dr. Chen has been an Associate Editor in the Conference Editorial Board of IEEE Control Systems Society since He is a founding member of the ASME subcommittee of "Fractional Dynamics" in He is a senior member of IEEE, a member of ASME and a member of ISIF (International Society for Information Fusion).